Differences between a Phasor and a Vector

If someone ask you whether current and voltage are vector or scalar quantity the obviously you will answer that they are scalar quantity. Next, the question arises if current and voltage are scalar quantity then why do we represent then in form of vector which is famously known as Phasor? We will discuss here this aspect.

Vectors are physical quantity which have magnitude, direction and above all which follows the triangle law of addition of two vectors. As current have both magnitude and direction but they do not follow the triangle law of addition of two vectors, hence current is a scalar. Same argument applies with voltage.

While representing a vector, it is represented by an arrow pointing toward a particular direction and the length of the arrow is proportional to the magnitude of the vector.

Now coming to Phasor.Electrical quantities such as voltage and current are scalar quantities. However, their values changes over time in a sinusoidal way.

V = VmSinωt

If we see this voltage on Voltage and Time axis, we find that magnitude of voltage varies from –Vm to +Vm with respect to time. Now consider the figure below.

In the figure a vector is drawn from the origin making an angle of wt with the time axis and rotating in anti clockwise direction. Mind that this vector is rotating with some frequency, that is why it is Phasor. Normal Vector do not rotate. If we take the projection of the vector on Voltage axis, we observe that we get the instantaneous value of the Voltage V = VmSinwt. It is normal practice to take the length of Phasor as the R.M.S value of the Voltage / Current while in vector, length is directly proportional to magnitude of the vector.

Anything that behaves like this can be represented by phasors, which are really just representations of sinusoids.

Thus Phasors are generally rotational representation of sinusoidally varying quantities. The phase differences in various sinusoidal quantities can be represented in space respectively by single elements rotating at angle difference with each other but their frequency should be same else they cannot be represented on a single diagram. Their projection on the reference axis gives the value of the individual quantities at an instant of time.

Hope it might help you. Thank you!

4 thoughts on “Differences between a Phasor and a Vector”

  1. Vectors and Phasors both are graphically represented as arrows pointing in a particular orientation. The length of each indicates the scalar value (speed, distance, force, voltage, current, etc.) of a represented parameter and both can be manipulated (example: added) similarly, but that’s where their similarity ends – the meaning of the “direction” they point differs.

    A vector represents a physical parameter characterized by both a scalar component (magnitude) and a direction in space. Vectors can be used to represent a velocity, flow, force, field or potential gradient, etc., at any moment and at any point in space – they exist in the moment and are independent of factors like frequency.

    Phasors represent the response and timing relationships within AC circuits or other systems operating at a single frequency after achieving steady state conditions (after transients have died down). Phasors differ from vectors in that the angular relationship between phasors (or between a phasor and a reference) represents their phase or timing relationships within a cycle, which under steady state conditions are invariant. Unlike vectors, the angles of a phasors don’t represent physical directions and have no physical meaning.

    Reply

Leave a Comment